In this section, the numerical calculations performed for the single cylinder geometry using the code implemented on FreeFEM++ [1]}, [2]} will be presented. FreeFEM++ requires the weak formulation of problems. Problem (REF )-() is then implemented as follows
\(\int _{\partial \mathcal {C}}v\,\sin (\theta )\,dS-\int _\mathcal {D}(\nabla \hat{p}\cdot \nabla v+k^2\hat{p}v)\,dV = 0, \forall v\) 
